If the phase error at each pixel in a complex-valued MRI image is known the noise in the image can be reduced resulting in improved detection of medically significant details. However, given a complex-valued MRI image, estimating the phase error at each pixel is a difficult problem. Several approaches have previously been suggested including non-linear least squares fitting and smoothing filters. We propose a new scheme based on iteratively applying a series of non-linear filters, each used to modify the estimate into greater agreement with one piece of knowledge about the problem, until the output converges to a stable estimate. We compare our results with other phase estimation and MRI denoising schemes using synthetic data.